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Results (12 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
1536.1-a2 1536.1-a \(\Q(\sqrt{3}) \) \( 2^{9} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $20.85795013$ 1.505292890 \( -\frac{61952}{9} a + \frac{162688}{9} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 155 a - 266\) , \( -1296 a + 2244\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(155a-266\right){x}-1296a+2244$
1536.1-c2 1536.1-c \(\Q(\sqrt{3}) \) \( 2^{9} \cdot 3 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.585986762$ $20.85795013$ 3.528326832 \( -\frac{61952}{9} a + \frac{162688}{9} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2149 a - 3722\) , \( -67356 a + 116664\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2149a-3722\right){x}-67356a+116664$
1536.1-v2 1536.1-v \(\Q(\sqrt{3}) \) \( 2^{9} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $17.42092743$ 2.514494285 \( -\frac{61952}{9} a + \frac{162688}{9} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 155 a - 266\) , \( 1296 a - 2244\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(155a-266\right){x}+1296a-2244$
1536.1-x2 1536.1-x \(\Q(\sqrt{3}) \) \( 2^{9} \cdot 3 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.012136362$ $17.42092743$ 2.545011098 \( -\frac{61952}{9} a + \frac{162688}{9} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2149 a - 3722\) , \( 67356 a - 116664\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2149a-3722\right){x}+67356a-116664$
3072.1-c2 3072.1-c \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $9.011399049$ 2.601366833 \( -\frac{61952}{9} a + \frac{162688}{9} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 10\) , \( 8 a - 16\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-10\right){x}+8a-16$
3072.1-h2 3072.1-h \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $9.011399049$ 1.300683416 \( -\frac{61952}{9} a + \frac{162688}{9} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 82 a - 142\) , \( 448 a - 776\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(82a-142\right){x}+448a-776$
3072.1-bx2 3072.1-bx \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.548725225$ $20.16139966$ 3.193632813 \( -\frac{61952}{9} a + \frac{162688}{9} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 10\) , \( -8 a + 16\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-10\right){x}-8a+16$
3072.1-cb2 3072.1-cb \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.366013255$ $20.16139966$ 4.260463665 \( -\frac{61952}{9} a + \frac{162688}{9} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 82 a - 142\) , \( -448 a + 776\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(82a-142\right){x}-448a+776$
4608.1-b2 4608.1-b \(\Q(\sqrt{3}) \) \( 2^{9} \cdot 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.792498913$ $16.46171389$ 3.766024158 \( -\frac{61952}{9} a + \frac{162688}{9} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 6449 a - 11169\) , \( -356440 a + 617372\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(6449a-11169\right){x}-356440a+617372$
4608.1-c2 4608.1-c \(\Q(\sqrt{3}) \) \( 2^{9} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $16.46171389$ 2.376043737 \( -\frac{61952}{9} a + \frac{162688}{9} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 463 a - 801\) , \( -7196 a + 12464\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(463a-801\right){x}-7196a+12464$
4608.1-bc2 4608.1-bc \(\Q(\sqrt{3}) \) \( 2^{9} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $7.357776513$ 1.062003562 \( -\frac{61952}{9} a + \frac{162688}{9} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 6449 a - 11169\) , \( 356440 a - 617372\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(6449a-11169\right){x}+356440a-617372$
4608.1-bf2 4608.1-bf \(\Q(\sqrt{3}) \) \( 2^{9} \cdot 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $2.035344004$ $7.357776513$ 4.323085168 \( -\frac{61952}{9} a + \frac{162688}{9} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 463 a - 801\) , \( 7196 a - 12464\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(463a-801\right){x}+7196a-12464$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.